In cardiovascular research there is an urgent need for methods which would quantitatively identify: regions of high shear stresses in the flow (hemolytic factor), regions of high and low stresses at the wall (atheromatic lesions), and separated or reverse flow regions (thrombogenic factors). A computer model capable of simulating physiologically important features of blood flow in vessels would be an indispensable research tool. The objective of this proposal is to develop such computer software. The computer model will be able to calculate three-dimensional time-dependent flow for an arbitrary vessel geometry including lesions and bifurcations, and a wide range of Reynolds numbers. Based on previous work, our approach will involve discretizing integral momentum and mass balance equations in primitive variables on a staggered, numerically generated boundary-conforming grid. Implicit formulation will provide numerical stability needed to resolve thin boundary layers. A special approximation for convective terms will eliminate numerical diffusion. The expected results of Phase I are the design of a two-dimensional version of the program and numerical experimentation to assess code's utility with respect to stated objective. The final three-dimensional version of the code will be developed in Phase II.